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Content material: Chapter 1 a number of version illustration (pages 1–40): Mohammed Chadli, Pierre Borne and Bernard DubuissonChapter 2 balance of continuing a number of versions (pages 41–64): Mohammed Chadli, Pierre Borne and Bernard DubuissonChapter three a number of version country Estimation (pages 65–98): Mohammed Chadli, Pierre Borne and Bernard DubuissonChapter four Stabilization of a number of types (pages 99–126): Mohammed Chadli, Pierre Borne and Bernard DubuissonChapter five strong Stabilization of a number of versions (pages 127–156): Mohammed Chadli, Pierre Borne and Bernard Dubuisson

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The obtained solution is also optimal for the initial problem in only the case where convex/nonconvex transformation occurs through equivalence. This remark is fundamental for interpreting the results obtained using optimization methods. In the next section we recall some of the main results of this formalism. 1. Linear matrix inequality formalism For a number of years, numerous studies within automation have been formulated in terms of convex optimization, implying linear matrix inequalities (LMI).

2. More precise determination of the operating classes of the system This new step enables the distribution into classes to be refined in order to obtain various operating ranges from which the base models will be identified [BOR 06, BOR 07]. 1. Classification using the Kohonen rule This is similar to the previous rule by simply making  (t )  0. From the class centers previously obtained, the classification is brought about by applying the following algorithm for each instance of vector x(t): g  arg min wk (t )  x(t ) k wg (t  1)  wg (t )   (t )( x(t )  wg (t )) wk (t  1)  wk (t )  k  g This operation is repeated until the weights are stabilized.

In the next section we recall some of the main results of this formalism. 1. Linear matrix inequality formalism For a number of years, numerous studies within automation have been formulated in terms of convex optimization, implying linear matrix inequalities (LMI). Reasons for the popularity of this approach include the existence of effective numeric resolution methods and the possibility of handling multicriteria synthesis. The following are some basic ideas for the LMI approach [BOY 94, CHI 96, RIC 01].